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I have recently started studying the basic ideas of symmetry and group representation in order to understand the basic principles behind the standard model. I do follow the difference between a global and a local symmetry and I do understand, in very general terms, the importance of local gauge symmetries in explaining basic features of the standard model.

But I would like to get clarification on the question below:

Is a hidden symmetry the same concept as a broken symmetry as regards the standard model?

Obviously hidden and broken are different words and so, to me at this stage, they imply different concepts within the SM framework.

The reason I am asking this question is that I get confused when I read statements on Wikipedia stating:

Hidden is perhaps a better term than broken.

The word perhaps worries me because it implies a subtle difference that I have not yet grasped.

I know that a hidden symmetry analogy is, for example, the basis for the flattened spiral arms of the milky way remaining in that shape possibly because of a dark matter halo surrounding them.

I know that an example of a broken symmetry is the differing masses given to different particles depending on how they couple to the Higgs field.

I cannot see, at the level I am at anyway, what motivates the Wikipedia article to adopt the wording it has, with respect to the SM.

As you will see from the comments below, anna v has provided me with a good link, which I really appreciate and which I am currently working my way through:

 

Everything in particle physics is hidden until it is revealed by a measurement :). try thisippp.dur.ac.uk/~krauss/Lectures/IntoToParticlePhysics/… 

but I wonder has Wikipedia got these ideas mixed up?

I am reposting this question, just in case anybody else has a defence of the Wikipedia wording.

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  • $\begingroup$ Who said "Hidden is perhaps a better term than broken"? I don't grasp the subtlety either... if there is one. $\endgroup$ – CuriousOne Jun 19 '15 at 7:05
  • $\begingroup$ Looks like a poorly written wikipedia article to me. I think the author had a real problem defining what symmetry breaking is and instead kept listing a number of disjoint examples. Worse, still, he was adding his own interpretation to it, which is really bad style in encyclopedic writing. $\endgroup$ – CuriousOne Jun 19 '15 at 7:32
  • $\begingroup$ Everything in particle physics is hidden until it is revealed by a measurement :). try this ippp.dur.ac.uk/~krauss/Lectures/IntoToParticlePhysics/… $\endgroup$ – anna v Jun 19 '15 at 13:06
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I am not sure what your hangup with the wording is. All these articles explain in painstaking detail that explicit breaking of a symmetry implies different masses and couplings, etc, and non-existence of conserved quantities (or violations of the corresponding conservation laws). You see that breaking in, e.g. flavor symmetries.

By contrast, spontaneous breaking is not "real" breaking, just "hiding" of the symmetries still there, ensuring renormalizability, miracles, etc. Yes, superficially, the patterns you are used to expect from symmetry, like equal masses, etc... are not there anymore, but you should focus on the things that do matter: conserved charges, currents, etc... So the equations are still symmetric, but their symmetry is hidden by changes of variables best suited to the vacuum structure of these theories--changes of variables do not alter the physics or the math, though---just the visibility of some features.

Formally, as emphasized in these articles, the SB symmetry is realized in the nonlinear Nambu-Goldstone mode, as opposed to the linear Wigner-Weyl mode, where the symmetry is apparent. Chiral symmetry in QCD and the EW symmetry are realized in this hidden Nambu-Goldstone mode. The whole point of SSB, however, is that the symmetry is still there, performing its delicate balancing act, mathematically: it is only hidden. "Perhaps" is a weasel word to placate the uncomprehending, that this is not "real" breaking, and to allow them to ignore the point, if they were resistant to it. Personally, I'd skip the "perhaps" which so offends you.

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